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If you are using wooden skewers, soak the skewers in water while you prepare the ingredients.
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Combine the garlic, lime juice, olive oil, paprika, salt and crushed red pepper flakes in a bowl. Place the marinade into a zipper sealable plastic bag and add the shrimp. Massage the marinade into the shrimp and let them marinate at room temperature for 30 minutes while you prepare the rest of the ingredients.
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Cut the onion into 1-inch pieces and separate the petals so you have individual squares of onion. Slice the chorizo into ½-inch thick slices.
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Assemble the skewers by placing a slice of chorizo in the curve of each shrimp. Run the skewer through one end of the shrimp, through the sausage and out through the other end of the shrimp. Place a square of onion on the skewer and then skewer another shrimp and chorizo slice. Repeat one more time with the onion and shrimp-chorizo slice.
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Pre-heat an outdoor grill or indoor grill pan. Your outdoor grill should be hot enough that you can only hold your hand 1-inch above the grill grates for 2 to 3 seconds before you want to pull it away.
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While the grill pre-heats, make the avocado-basil dip by pulsing the avocado in a mini chopper. Add the remaining ingredients and purée until smooth. Thin with a little water or more lime juice if needed and season to taste with salt. Transfer the dip to a small bowl.
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Place the shrimp and chorizo skewers on the grill and cook for 2 to 3 minutes per side, or until shrimp are cooked through and firm to the touch.
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Serve with the avocado-basil dip next to the skewers or if you’ve thinned the dip with enough lime juice and water, drizzle some of it across the skewers before serving and scatter chopped fresh basil leaves on top.